Funny thing is, we are all comparing apples to oranges. Not all tires are created equal. Even among the major subgroups, there are many variations. My Ford 1510 came with the old Firestone Turf and Field R3 tires, which, sadly are no longer available. I replaced the fronts with Carlisle, which are fine, but the spacing between the lugs are much finer, thus, they clog easier. Then there are diamond treads, bar turfs, etc... These various tread adaptations all had the expressed purpose of operating on a lawn with minimum damage to the lawn. Of course traction would be a secondary concern, as these were meant as a lawn care tire, but the different tread patterns within this group will perform differently under different conditions. The compact utility tractor demands more out of a tire than a lawn mower typically would.
The R4 tire has been designed from the get go to be very slash and puncture resistant when operating under heavy loads typical of heavy construction equipment. This requires them to have thick, stiff sidewalls and even thicker treads. Typically a harder rubber compound would also be expected to be used for this very purpose. Thick, wide tread bars would be a logical choice for construction equipment that would be expected to drive all over broken up concrete, twisted metal and broken glass, as well as nails, screws and other errata. Was traction the primary objective? Of course not. But it had to bee "good enough" to get the job done. Once again, different variations within this group have attempted to address the traction issues for the ever expanding role of the compact utility tractor.
Same holds true with R1. Many variations within this design. All have merit based on their designated design objectives. Maximum traction was the primary consideration, as these directional tread tires had one specific goal in mind: Pull heavy ground engaging implements through the earth. Different variations have been introduced within this category to address different soil types. Do they all perform the same? Of course not, but they do pull better than the other two major types. Of course, the obvious drawbacks are lower load capacity when using a FEL and the tendency to tear up the lawn. Of course, the tire manufacturers have been addressing these issues with different ply ratings and tread widths. Once again, no two are alike.
I guess my point is the CUT has blurred the lines of traditional purpose built machinery into something that does everything. Designing a tire that will truly do everything best is an impossible task, and as such, the tire manufacturers really have their work cut out for them. All R1's are not created equal, nor are all R3's or R4's; and to say all R3's have better/worse traction than all R4's would be ridiculous. The best we can do is find the compromise that works best for our particular needs.
Joe